




from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403





def        __UpperCAmelCase						(							lowerCamelCase_ :     str  ,							lowerCamelCase_ :     complex  ,							lowerCamelCase_ :     str = "x"  ,							lowerCamelCase_ :     float = 10**-10  ,							lowerCamelCase_ :     int = 1  ,							)       ->  complex:







			"""simple docstring"""





			SCREAMING_SNAKE_CASE_   : Optional[Any]					  =      symbols(lowerCamelCase_  )
			SCREAMING_SNAKE_CASE_   : int					  =      lambdify(lowerCamelCase_  ,							lowerCamelCase_  )
			SCREAMING_SNAKE_CASE_   : Union[str, Any]					  =      lambdify(lowerCamelCase_  ,							diff(lowerCamelCase_  ,							lowerCamelCase_  )  )

			SCREAMING_SNAKE_CASE_   : Dict					  =      starting_point

			while True:
						if diff_function(lowerCamelCase_  ) != 0:
									SCREAMING_SNAKE_CASE_   : Optional[int]					  =      prev_guess - multiplicity * func(lowerCamelCase_  ) / diff_function(
									    lowerCamelCase_  )
						else:
									raise ZeroDivisionError('Could not find root'  ) from None

						# Precision is checked by comparing the difference of consecutive guesses
						if abs(next_guess - prev_guess  ) < precision:
									return next_guess

						SCREAMING_SNAKE_CASE_   : str					  =      next_guess


# Let's Execute
if __name__ == "__main__":
						# Find root of trigonometric function
						# Find value of pi
						print(F"""The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}""")

						# Find root of polynomial
						# Find fourth Root of 5
						print(F"""The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5j)}""")

						# Find value of e
						print(
						    '''The root of log(y) - 1 = 0 is ''',
						    F"""{newton_raphson("log(y) - 1", 2, variable="y")}""",
						)

						# Exponential Roots
						print(
						    '''The root of exp(x) - 1 = 0 is''',
						    F"""{newton_raphson("exp(x) - 1", 10, precision=0.0_05)}""",
						)

						# Find root of cos(x)
						print(F"""The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}""")











"""simple docstring"""
import os
from shutil import copyfile
from typing import List, Optional, Tuple

from ...tokenization_utils import AddedToken
from ...tokenization_utils_fast import PreTrainedTokenizerFast
from ...utils import is_sentencepiece_available, logging


if is_sentencepiece_available():
 from .tokenization_big_bird import BigBirdTokenizer
else:
 snake_case : Tuple     		=		None

snake_case : Tuple     		=		logging.get_logger(__name__)
snake_case : List[Any]     		=		{"""vocab_file""": """spiece.model""", """tokenizer_file""": """tokenizer.json"""}

snake_case : Dict     		=		{
    """vocab_file""": {
        """google/bigbird-roberta-base""": """https://huggingface.co/google/bigbird-roberta-base/resolve/main/spiece.model""",
        """google/bigbird-roberta-large""": (
            """https://huggingface.co/google/bigbird-roberta-large/resolve/main/spiece.model"""
        ),
        """google/bigbird-base-trivia-itc""": (
            """https://huggingface.co/google/bigbird-base-trivia-itc/resolve/main/spiece.model"""
        ),
    },
    """tokenizer_file""": {
        """google/bigbird-roberta-base""": (
            """https://huggingface.co/google/bigbird-roberta-base/resolve/main/tokenizer.json"""
        ),
        """google/bigbird-roberta-large""": (
            """https://huggingface.co/google/bigbird-roberta-large/resolve/main/tokenizer.json"""
        ),
        """google/bigbird-base-trivia-itc""": (
            """https://huggingface.co/google/bigbird-base-trivia-itc/resolve/main/tokenizer.json"""
        ),
    },
}

snake_case : int     		=		{
    """google/bigbird-roberta-base""": 4_0_9_6,
    """google/bigbird-roberta-large""": 4_0_9_6,
    """google/bigbird-base-trivia-itc""": 4_0_9_6,
}


snake_case : List[str]     		=		"""▁"""



class        UpperCamelCase__ (				a_):







    """simple docstring"""
    __UpperCAmelCase           = VOCAB_FILES_NAMES
    __UpperCAmelCase           = PRETRAINED_VOCAB_FILES_MAP
    __UpperCAmelCase           = PRETRAINED_POSITIONAL_EMBEDDINGS_SIZES
    __UpperCAmelCase           = BigBirdTokenizer
    __UpperCAmelCase           = ["""input_ids""", """attention_mask"""]
    __UpperCAmelCase           = []







    def __init__(		self :	Optional[int]				,    UpperCamelCase_ :	int=None				,    UpperCamelCase_ :	Dict=None				,    UpperCamelCase_ :	int="<unk>"				,    UpperCamelCase_ :	Tuple="<s>"				,    UpperCamelCase_ :	int="</s>"				,    UpperCamelCase_ :	Union[str, Any]="<pad>"				,    UpperCamelCase_ :	Optional[Any]="[SEP]"				,    UpperCamelCase_ :	int="[MASK]"				,    UpperCamelCase_ :	Tuple="[CLS]"				,    **UpperCamelCase_ :	Optional[Any]				,    ):





           '''simple docstring'''

           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else bos_token
           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else eos_token
           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else unk_token
           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else pad_token
           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else cls_token
           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else sep_token

           # Mask token behave like a normal word, i.e. include the space before it
           __magic_name__      				=    AddedToken(UpperCamelCase_				,    lstrip=UpperCamelCase_				,    rstrip=UpperCamelCase_ ) if isinstance(UpperCamelCase_				,    UpperCamelCase_ ) else mask_token

           super().__init__(
               UpperCamelCase_				,    tokenizer_file=UpperCamelCase_				,    bos_token=UpperCamelCase_				,    eos_token=UpperCamelCase_				,    unk_token=UpperCamelCase_				,    sep_token=UpperCamelCase_				,    pad_token=UpperCamelCase_				,    cls_token=UpperCamelCase_				,    mask_token=UpperCamelCase_				,    **UpperCamelCase_				,    )

           __magic_name__      				=    vocab_file
           __magic_name__      				=    False if not self.vocab_file else True







    def 				a__			(		self :	Union[str, Any]				,    UpperCamelCase_ :	List[int]				,    UpperCamelCase_ :	Optional[List[int]] = None ):





           '''simple docstring'''

           __magic_name__      				=    [self.sep_token_id]
           __magic_name__      				=    [self.cls_token_id]
           if token_ids_a is None:
                  return cls + token_ids_a + sep
           return cls + token_ids_a + sep + token_ids_a + sep







    def 				a__			(		self :	Optional[Any]				,    UpperCamelCase_ :	List[int]				,    UpperCamelCase_ :	Optional[List[int]] = None				,    UpperCamelCase_ :	bool = False ):





           '''simple docstring'''

           if already_has_special_tokens:
                  if token_ids_a is not None:
                         raise ValueError(
                             'You should not supply a second sequence if the provided sequence of '
                             'ids is already formatted with special tokens for the model.' )
                  return [1 if x in [self.sep_token_id, self.cls_token_id] else 0 for x in token_ids_a]

           if token_ids_a is None:
                  return [1] + ([0] * len(UpperCamelCase_ )) + [1]
           return [1] + ([0] * len(UpperCamelCase_ )) + [1] + ([0] * len(UpperCamelCase_ )) + [1]







    def 				a__			(		self :	Optional[Any]				,    UpperCamelCase_ :	List[int]				,    UpperCamelCase_ :	Optional[List[int]] = None ):





           '''simple docstring'''

           __magic_name__      				=    [self.sep_token_id]
           __magic_name__      				=    [self.cls_token_id]

           if token_ids_a is None:
                  return len(cls + token_ids_a + sep ) * [0]
           return len(cls + token_ids_a + sep ) * [0] + len(token_ids_a + sep ) * [1]







    def 				a__			(		self :	Union[str, Any]				,    UpperCamelCase_ :	str				,    UpperCamelCase_ :	Optional[str] = None ):





           '''simple docstring'''

           if not self.can_save_slow_tokenizer:
                  raise ValueError(
                      'Your fast tokenizer does not have the necessary information to save the vocabulary for a slow '
                      'tokenizer.' )

           if not os.path.isdir(UpperCamelCase_ ):
                  logger.error(f"""Vocabulary path ({save_directory}) should be a directory""" )
                  return
           __magic_name__      				=    os.path.join(
               UpperCamelCase_				,    (filename_prefix + '-' if filename_prefix else '') + VOCAB_FILES_NAMES['vocab_file'] )

           if os.path.abspath(self.vocab_file ) != os.path.abspath(UpperCamelCase_ ):
                  copyfile(self.vocab_file				,    UpperCamelCase_ )

           return (out_vocab_file,)